Thursday, 12 April 2012

Economists need taught about physical constraints - but physicists need to learn about prices

Another excellent post from Tom Murphy entitled "Exponential Economist Meets Finite Physicist" is causing some interest. In the post the point is made that exponentially increasing use of energy is impossible, and that economic growth without energy use growth is difficult to imagine. These issues need to be more widely considered within economics, especially in these times of depressed output amid high energy prices. They are not simply for 400 years hence but are worth considering now - see relatively recent New Scientist article "How Clean is Green Energy?".

However certain points are made in the post that I don't think are justified and which are the sort of thing that is frequently stated without sufficient analysis at (informative and interesting) places like The Oil Drum and Our Finite World.

First of all, it is asserted that "If the flow of energy is fixed, but we posit continued economic growth, then GDP continues to grow while energy remains at a fixed scale. This means that energy—a physically-constrained resource, mind—must become arbitrarily cheap as GDP continues to grow and leave energy in the dust." This cannot be simply asserted - within most models it's simply not true, and the models in which it is true are the most unrealistic models (we would need elastic substitution of energy and other factor inputs but it appears that other factors can only substitute for energy on a very inelastic basis).

The baseline, first-order model of economic growth is the Ramsey model with Cobb-Douglas production and logarithmic utility (which the representative agent maximises in order to make consumption/investment decisions). If we suppose a constant returns to scale Cobb-Douglas production function with labour (fixed), energy (fixed) and capital (endogenous) subject to some exponentially growing productivity (*), then we derive a balanced growth path in which output, consumption and capital stock all grow at the rate of productivity growth (despite fixed labour and energy implying effective diminishing returns). The prices of the factors of production on the balanced growth path in this model are: constant for capital (i.e. interest rate is a positive constant); exponentially growing (at the rate of productivity growth) for energy and labour. This is because under Cobb-Douglas production, factors earn a constant share of output i.e. payments to energy are constant as a share of output, but the quantity of energy used is constant whilst output is exponentially growing: therefore energy's price must be exponentially growing.

So the first order model for describing economic growth predicts that if we had an economy with fixed energy inputs but positive economic growth, then energy prices would be growing, not falling. The post then relies on a floor for energy prices as it's mechanism in generating subsequent phenomena: but economic growth with constant energy input implies growing prices that do not run into this floor constraint, so the rest of the argument does not necessarily follow.

The post then also repeats various assertions that have been made for a steady state economy: "it’s not your father’s growth. It’s not ... , interest on bank accounts, loans, fractional reserve money, investment." I'm not sure where the idea comes from that a positive rate of interest on bank accounts relies on economic growth, but it's a meme that I've seen expressed before. It doesn't seem logical to me: a simple case is a model of generations in which the young work, consume and save (i.e. make loans) whilst the old consume out of their savings. These savings/loans are just pieces of paper so in reality the young work and their earnings provide the consumption goods for themselves and the older generation. The interest rate on the savings is just a price(**) that agents take when splitting their consumption from their own earnings into consumption whilst young and consumption whilst old - a high interest rate is perfectly compatible with a steady state economy if agents have a high rate of time preference. Fractional reserve banking likewise has nothing to do with economic growth. 

The post is fantastic at outlining an issue that economists have not grappled with, but in considering the economic impacts of the issue, the article makes clear a need for economists to provide some of the analysis!

(*) I'm not saying that this is a good model of long term growth, in particular I agree with this criticism of Noah Smith: "
Step 1: Take the parts of the economy you can't explain (i.e. the residuals) and label them either "culture" or "technology".
Step 2: Make ultra-confident pronouncements about the future behavior of culture and/or technology.
What I don't like, first of all, is that Step 2 just never makes any sense. The thing you are calling "culture" or "technology" is precisely the part that you couldn't explain with your models. Hence, it is the least likely thing for you to be able to predict going forward.
Admit it, economists: You don't know what is going to happen with technology. You don't know what is going to happen with culture. If you did, you would have included those things as endogenous variables in the model instead of simply labeling the residual."

(**) Though in steady state equilibrium it will be a positive function of both the growth rate and the rate of time preference.


  1. I think you've misunderstood the original post. Look at the conversation:

    Physicist: "energy...must become arbitrarily cheap as GDP continues to grow and leave energy in the dust."

    Economist: "Yes"

    Physicist: "Wow. Do you really believe that?"

    In other words, the physicist put that false assertion forward as a trap. It's the economist who failed to understand price formation. Why the economist would make such a mistake, if indeed the report is accurate, I cannot imagine. Perhaps he was caught off guard, having always thought that energy would eventually become an abundant resource and thus cease to be economically important.

    Btw regarding your model of generations, who buys the loans and pays the interest?

    1. No, Tom Murphy has put forward the idea before that energy prices must decline if growth is to continue. For example: "Consequently, the price of food, energy, and manufacturing would drop to negligible levels relative to the fluffy stuff. And is this realistic—that a vital resource at its physical limit gets arbitrarily cheap? Bizarre." from So it wasn't a trap - that's how he views the prices necessary in a world of fixed energy inputs but growth in output.

      In the generation model a zero profit making financial intermediary buys the loans and pays the interest. It's a model that reveals flaws in the assumption that debt and interest depend upon economic growth, not a realistic model of the real world.

    2. Correct me if I'm wrong, but is it not so that in the long run, as fixed factors of production capture an increasingly large share of output, capital accumulation slows down to a point where it equals capital depreciation, at which point economic growth stops? I think this is the situation that Murphy is talking about. The only way to avoid this situation would be if energy prices declined, which both Murphy and you point out to be a bizarre proposition.

      I appreciate that you modeled energy as a fixed factor of production, which makes this long-run outcome apparent. From what I have seen, growth models usually just ignore energy altogether, which might explain why the Economist was caught off guard. That is, he was tricked into agreeing that energy prices relative to production would fall into obscurity -- a bizarre proposition.

      Regarding your generation model, I'm not sure I understand. Where does the financial intermediary get the money to pay the interest? Could you point me to a paper or other resource that describes this particular model?

    3. But if production is CRS Cobb-Douglas then factors are paid a constant share of output, not an increasingly large share.

      A more realistic production function is CES with inelastic substitution of energy with capital (see for example prodution functions). Under this model, the share paid to energy tends to 100% and the growth rate of capital tends to zero. However, even here we have some economic growth due to productivity growth (again, I'm not claiming that this productivity growth in the face of constant factors is likely. I'm just saying that Tom Murphy's article appeared to have a proof of the impossibility of growth under fixed factors due to price effects, but this proof is flawed and the price effects do not work as claimed).

      The generations model is based on the standard OLG model (introduced by Diamond in 1965) - see 2nd Chapter of Advanced Macroeconomics by David Romer but assume growth rates are zero.

  2. Comment from Dikran (Blogger failed to allow it to be posted for some reason):

    Your criticism of Tom Murphy's argument is correct, but could be stated more simply. He argues that energy cannot become an arbitrarily small percentage of GDP; you point out that this is not true, or at least not obvious.

    The essence of his argument that energy cannot be an arbitrarily small percentage of GDP is, "But if energy became arbitrarily cheap, someone could buy all of it".

    This is clearly false, as it takes a marginal price for a tiny amount of energy and scales it up to produce a total price for the purchase of all energy output everywhere. One can try to corner the market, but this is not the way to estimate the price of doing so.

    Of course this is the same as your criticism. I have just distilled out the reference to various economic models with which readers may be unfamiliar.